My Achilles tendon always hurts. Does it have to do with the type of shoes?

It can. Shoes of varying types can cause pain to the achilles attachment (tendon) or associated bursa. Several mechanisms can produce this from lack of arch support if you pronate to repetitive direct heel contact with the back part of the shoe. See a local foot specialist and they should be able to help.
Achilles tendon. Depends on the site of exact pain, is it near its insertion or away from its insertion.